Information on Result #599500
There is no digital (50, 190, 251)-net over F4, because extracting embedded orthogonal array would yield linear OA(4190, 251, F4, 140) (dual of [251, 61, 141]-code), but
- residual code [i] would yield OA(450, 110, S4, 35), but
- the linear programming bound shows that M ≥ 2843 632588 461264 124732 153811 225362 179218 741807 134663 046707 045169 984379 030584 774721 441671 432589 217156 300800 / 1967 445154 431728 253949 288537 958066 067140 960836 153380 308963 321499 990743 635853 > 450 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (50, 191, 251)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (50, 192, 251)-net over F4 | [i] | ||
| 3 | No digital (50, 193, 251)-net over F4 | [i] | ||